The mechanism of bacterial inactivation by electric discharges (non-thermal plasma) is examined on the basis of the action of the formed peroxynitrite and hydrogen peroxide on the external membrane of bacteria. A model accounts for the gas to liquid transfer of the active species which react with the bacterial wall at the liquid surface or /and in the bulk solution. Direct exposure to the glidarc discharge induces a pseudo zero order decay of the bacterial concentration, followed by a pseudo 1st order step for low concentrations. Post-discharge reactions develop after switching off the discharge according to a 1st order mechanism and show that active species drift in the solution. Additionally the bactericidal properties of pure water exposed to the discharge (i.e., ``Plasma Activated Water'') was evidenced even 24 h after performing the plasma treatment.